Research On Selection Rule Set For Driver Nodes Based On The Structure Of Networks

Structural controllability is a concept proposed in terms of the topology of real networks.The research on structural controllability can give some guidance before we quantitatively investigate the controllability of a real network,so as to provide a feasible reference for controlling the real network.One of the most important topics on structural controllability is to find the minimum number of driver nodes which can guarantee the network structurally controllable.In practical applications,it sometimes has been known that driving some nodes can make the system structurally controllable.However,due to the consideration of lower control cost,it is always desirable to select the least number of nodes from known node set as driver nodes such that the system is still structurally controllable.To solve this problem,the elimination and supplement algorithms giving complete control schemes will be introduced respectively in this paper.The algorithms are based on two algebraic criteria of structural controllability,that is,all of the driver nodes selection rules are solved based on the input connectivity condition and full row rank condition.This paper focuses on how to improve the computational efficiency as much as possible on the basis of ensuring the completeness of driver nodes selection rule set.Dimension reducing and simplication algorithm,partial backtracking algorithm,new lower triangularization algorithm,etc.are given in this paper,as well as the illustration of the correctness of these algorithms.Furthermore,in practical applications,besides of the problem of structural controllability,there are some other problems such as partially structural controllability and structural transittability.While the former means that only a part of the nodes in the system need to be controllable,and the latter means that the system nodes need to be transferred to a specific state rather than arbitrary states.Based on the criteria for these two properties,algorithms for selecting driver nodes to make the system satisfy partially structural controllability and structural transittability are presented respectively.Moreover,in order to analyze the effectiveness of the above algorithms,we design some simulation tests of using them for some real networks and randomly-generated networks,and compare the performances of related algorithms.